Aesop's FablesMoral:Slow and SteadyWins the Race

Other ways of saying it:The race is not always to the swift.Persistence wins out.You can rest when you're done.Don't be over-confident.Keep on keepin' on!

Aesop's Fable:

The Tortoise and the Hare

A
Hare one day ridiculed the short legs and slow pace of the Tortoise,
who replied, laughing: “You might be fast, but I will beat you in a
race.”

The Hare thought this was ridiculous and accepted the challenge.

Both
the Tortoise and the Hare agreed to let the Fox decide where the race
should begin and end and what course it should follow.

The Hare took a rest beside the racecourse and fell fast asleep.

When
he finally woke up and resumed racing to the end, he saw that the
Tortoise had already finished...and was now napping happily and
comfortably.

Another version

In The Aesop for Children,
illustrated by Milo Winter, there's a translation that places us much
more in the mindset of the Hare, which I find a great deal more fun and
involving. Appropriately, this one is entitled

The Hare and the Tortoise

A Hare was making fun of the Tortoise one day for being so slow.

"Do you ever get anywhere?" he asked with a mocking laugh.

"Yes," replied the Tortoise, "and I get there sooner than you
think. I'll run you a race and prove it."

The Hare was much amused at the idea of running a race with the
Tortoise, but for the fun of the thing he agreed. So the Fox, who
had consented to act as judge, marked the distance and started
the runners off.

The Hare was soon far out of sight, and to make the Tortoise feel
very deeply how ridiculous it was for him to try a race with a
Hare, he lay down beside the course to take a nap until the
Tortoise should catch up.

The Tortoise meanwhile kept going slowly but steadily, and, after
a time, passed the place where the Hare was sleeping. But the
Hare slept on very peacefully; and when at last he did wake up,
the Tortoise was near the goal. The Hare now ran his swiftest,
but he could not overtake the Tortoise in time.

The Hare and the Tortoise summary:

The Tortoise and the Hare may be Aesop's most famous fable, and "Slow but steady" his most famous moral.

(Though in the 2nd version above, the moral is given as "The race is not always to the swift." While "slow and steady wins the race" is an encouragement to the tortoises among us, "the race is not always to the swift" serves more as an admonition to the hares!")

I've
often heard a version told that has the hare challenging the tortoise,
but note that Aesop's intent in the versions above is that the challenge is Tortoise's,
resulting from Hare's contemptuous taunts.

Note also that Tortoise expects to win!

Taken from Hare's point of view, the fable's message is a warning against over-confidence, though there really isn't enough information in the fable about Hare to tell us why Tortoise thought he could win. That's why when you read or see the story told in popular media, there's usually a lot more to it!